Power-Law Phenomena in Adhesive De-Bonding

1996 ◽  
Vol 458 ◽  
Author(s):  
G. Kendall ◽  
P. J. Cote ◽  
D. Crayon ◽  
F. J. Bonetto
Keyword(s):  
Power Law ◽  
Characteristic Length ◽  
Power Laws ◽  
Structural Features ◽  
Fractal Nature ◽  
Pressure Sensitive Adhesive ◽  
Self Organized ◽  
Pressure Sensitive ◽  
Self Organized Criticality ◽  
Glass Interface

ABSTRACTAcoustic emission (AE) events were recorded during the peeling of pressure-sensitive adhesive (PSA) tape from a silicate glass surface. The distributions of AE event durations and energies are found to have the form of power laws. Power-law dependencies (hyperbolic distributions) are recognized as a consequence of self-organized criticality (SOC), resulting from the absence of any characteristic length or time scales. In these studies, standard optical microscopy was used to characterize the fractal nature of the PSA-glass interface. The present results suggest that it is the inherent static structural features found at the fractal PSA-glass interface which produce the observed hyperbolic distributions in AE events, rather than a true SOC process.

DYNAMICAL EXPLANATION FOR THE EMERGENCE OF POWER LAW IN A STOCK MARKET MODEL

1996 ◽  
Vol 07 (01) ◽  
pp. 65-72 ◽  
Author(s):  
MOSHE LEVY ◽  
SORIN SOLOMON ◽  
GIVAT RAM
Keyword(s):  
Stock Market ◽  
Power Law ◽  
Wealth Distribution ◽  
Power Laws ◽  
Stationary Regime ◽  
Market Model ◽  
Self Organized ◽  
Wide Range ◽  
Self Organized Criticality ◽  
Sand Piles

Power laws are found in a wide range of different systems: From sand piles to word occurrence frequencies and to the size distribution of cities. The natural emergence of these power laws in so many different systems, which has been called self-organized criticality, seems rather mysterious and awaits a rigorous explanation. In this letter we study the stationary regime of a previously introduced dynamical microscopic model of the stock market. We find that the wealth distribution among investors spontaneously converges to a power law. We are able to explain this phenomenon by simple general considerations. We suggest that similar considerations may explain self-organized criticality in many other systems. They also explain the Levy distribution.

scholarly journals Stairway to Self-Organized Criticality: SOC on a Slope using Relative Critical Heights

2008 ◽  
Vol 6 (4) ◽  
Author(s):  
Clinton Davis
Keyword(s):  
Computational Model ◽  
Power Law ◽  
Gaussian Distribution ◽  
Power Laws ◽  
Snow Avalanches ◽  
Self Organized ◽  
Self Organized Criticality ◽  
Relative Differences

A computational model of loose snow avalanches was studied as an example of Self-Organized Criticality (SOC). The distribution of the magnitudes of avalanches was measured for a stair-stepped system with various critical relative differences and system slopes. Depending on the configuration, the model showed either power law behaviors or a Gaussian distribution. For configurations that displayed power laws, the slope of the power law was dependent on the configuration of the system.

scholarly journals Associating an Entropy with Power-Law Frequency of Events

Entropy ◽  
2018 ◽  
Vol 20 (12) ◽  
pp. 940 ◽  
Author(s):  
Evaldo Curado ◽  
Fernando Nobre ◽  
Angel Plastino
Keyword(s):  
Information Theory ◽  
Forest Fires ◽  
Ground State ◽  
State Energy ◽  
Power Laws ◽  
Natural Systems ◽  
Self Organized ◽  
Self Organized Criticality ◽  
Isothermal Processes ◽  
Entropic Index

Events occurring with a frequency described by power laws, within a certain range of validity, are very common in natural systems. In many of them, it is possible to associate an energy spectrum and one can show that these types of phenomena are intimately related to Tsallis entropy S q . The relevant parameters become: (i) The entropic index q, which is directly related to the power of the corresponding distribution; (ii) The ground-state energy ε 0 , in terms of which all energies are rescaled. One verifies that the corresponding processes take place at a temperature T q with k T q ∝ ε 0 (i.e., isothermal processes, for a given q), in analogy with those in the class of self-organized criticality, which are known to occur at fixed temperatures. Typical examples are analyzed, like earthquakes, avalanches, and forest fires, and in some of them, the entropic index q and value of T q are estimated. The knowledge of the associated entropic form opens the possibility for a deeper understanding of such phenomena, particularly by using information theory and optimization procedures.

scholarly journals Observational evidence in favor of scale-free evolution of sunspot groups

2018 ◽  
Vol 618 ◽  
pp. A183
Author(s):  
A. Shapoval ◽  
J.-L. Le Mouël ◽  
M. Shnirman ◽  
V. Courtillot
Keyword(s):  
Weibull Distribution ◽  
Power Law ◽  
Large Range ◽  
Scale Free ◽  
Self Organized ◽  
Self Organized Criticality ◽  
Spatio Temporal ◽  
Computational Procedures ◽  
Definition Of ◽  
Sunspot Groups

Context. The hypothesis stating that the distribution of sunspot groups versus their size (φ) follows a power law in the domain of small groups was recently highlighted but rejected in favor of a Weibull distribution. Aims. In this paper we reconsider this question, and are led to the opposite conclusion. Methods. We have suggested a new definition of group size, namely the spatio-temporal “volume” (V) obtained as the sum of the observed daily areas instead of a single area associated with each group. Results. With this new definition of “size”, the width of the power-law part of the distribution φ ∼ 1/Vβ increases from 1.5 to 2.5 orders of magnitude. The exponent β is close to 1. The width of the power-law part and its exponent are stable with respect to the different catalogs and computational procedures used to reduce errors in the data. The observed distribution is not fit adequately by a Weibull distribution. Conclusions. The existence of a wide 1/V part of the distribution φ suggests that self-organized criticality underlies the generation and evolution of sunspot groups and that the mechanism responsible for it is scale-free over a large range of sizes.

Self-Organized Criticality and Dynamic Instability of Microtubule Growth

1995 ◽  
Vol 50 (9-10) ◽  
pp. 739-740 ◽  
Author(s):  
Peter Babinec ◽  
Melánia Babincová
Keyword(s):  
Power Law ◽  
Dynamic Instability ◽  
Relative Number ◽  
Self Organized ◽  
Self Organized Criticality ◽  
Microtubule Growth

Abstract We have shown that the distribution of lengths of site nucleated microtubules obey an algebraic power law relationship D(s) = As-τ, where D(s) is relative number of microtubules with length 5, A and τ are constants. This relationship indicates the possibility of a self-organized criticality in the dynamic instability of microtubule growth

SELF-ORGANIZED CRITICALITY AND THE BARKHAUSEN EFFECT IN AMORPHOUS AND POLYCRYSTALLINE METALS

1993 ◽  
Vol 07 (01n03) ◽  
pp. 934-937 ◽  
Author(s):  
PAUL J. COTE ◽  
LAWRENCE V. MEISEL
Keyword(s):  
Power Law ◽  
Barkhausen Effect ◽  
Self Organized ◽  
Polycrystalline Metals ◽  
Power Spectral ◽  
Power Spectral Densities ◽  
Spatially Extended ◽  
Self Organized Criticality ◽  
Dissipative Dynamical Systems ◽  
Pulse Energies

An investigation of the possibility that the Barkhausen effect in amorphous and polycrystalline ferromagnets is an example of self-organized criticality is described. Since the theory of self-organized criticality was introduced by Bak, Tang, and Weisenfeld to explain the behavior of spatially extended, dissipative, dynamical systems the Barkhausen effect is a natural candidate for such a description. The data are consistent with self-organized critical behavior: the power spectral densities depend on frequency f as 1/fa and the distribution of pulse energies are well described by a power law analogous to the Gutenberg-Richter law for earthquakes. Alternative explanations for power law dependences are also presented.

SELF-ORGANIZED CRITICALITY MODEL FOR EARTHQUAKES: QUIESCENCE, FORESHOCKS AND AFTERSHOCKS

1999 ◽  
Vol 09 (12) ◽  
pp. 2249-2255 ◽  
Author(s):  
S. HAINZL ◽  
G. ZÖLLER ◽  
J. KURTHS
Keyword(s):  
Power Law ◽  
B Value ◽  
Power Law Distribution ◽  
Aftershock Activity ◽  
Omori Law ◽  
Self Organized ◽  
Spatiotemporal Clustering ◽  
Self Organized Criticality ◽  
Clustering Of Events ◽  
Foreshock Activity

We introduce a crust relaxation process in a continuous cellular automaton version of the Burridge–Knopoff model. Analogously to the original model, our model displays a robust power law distribution of event sizes (Gutenberg–Richter law). The principal new result obtained with our model is the spatiotemporal clustering of events exhibiting several characteristics of earthquakes in nature. Large events are accompanied by a precursory quiescence and by localized fore- and aftershocks. The increase of foreshock activity as well as the decrease of aftershock activity follows a power law (Omori law) with similar exponents p and q. All empirically observed power law exponents, the Richter B-value, p and q and their variability can be reproduced simultaneously by our model, which depends mainly on the level of conservation and the relaxation time.

scholarly journals Entropy production and self-organized (sub)criticality in earthquake dynamics

2010 ◽  
Vol 368 (1910) ◽  
pp. 131-144 ◽  
Author(s):  
Ian G. Main ◽  
Mark Naylor
Keyword(s):  
Numerical Model ◽  
Entropy Production ◽  
Power Law ◽  
Subcritical State ◽  
Earthquake Dynamics ◽  
Broad Bandwidth ◽  
Rupture Area ◽  
Self Organized ◽  
Self Organized Criticality ◽  
Definition Of

We derive an analytical expression for entropy production in earthquake populations based on Dewar’s formulation, including flux (tectonic forcing) and source (earthquake population) terms, and apply it to the Olami–Feder–Christensen numerical model for earthquake dynamics. Assuming the commonly observed power-law rheology between driving stress and remote strain rate, we test the hypothesis that maximum entropy production (MEP) is a thermodynamic driver for self-organized ‘criticality’ (SOC) in the model. MEP occurs when the global elastic strain is near-critical, with small relative fluctuations in macroscopic strain energy expressed by a low seismic efficiency, and broad-bandwidth power-law scaling of frequency and rupture area. These phenomena, all as observed in natural earthquake populations, are hallmarks of the broad conceptual definition of SOC (which has, to date, often included self-organizing systems in a near but strictly subcritical state). In the MEP state, the strain field retains some memory of past events, expressed as coherent ‘domains’, implying a degree of predictability, albeit strongly limited in practice by the proximity to criticality and our inability to map the natural stress field at an equivalent resolution to the numerical model.

scholarly journals SIMULATION OF MAJORITY RULE DISTURBED BY POWER-LAW NOISE ON DIRECTED AND UNDIRECTED BARABÁSI–ALBERT NETWORKS

2008 ◽  
Vol 19 (07) ◽  
pp. 1063-1067 ◽  
Author(s):  
F. W. S. LIMA
Keyword(s):  
Power Law ◽  
Majority Rule ◽  
Noise Spectrum ◽  
Square Lattice ◽  
Complex Environment ◽  
Time Step ◽  
Disorder Phase Transition ◽  
Self Organized ◽  
Self Organized Criticality ◽  
Power Law Noise

On directed and undirected Barabási–Albert networks the Ising model with spin S = 1/2 in the presence of a kind of noise is now studied through Monte Carlo simulations. The noise spectrum P(n) follows a power law, where P(n) is the probability of flipping randomly select n spins at each time step. The noise spectrum P(n) is introduced to mimic the self-organized criticality as a model influence of a complex environment. In this model, different from the square lattice, the order-disorder phase transition of the order parameter is not observed. For directed Barabási–Albert networks the magnetisation tends to zero exponentially and undirected Barabási–Albert networks remain constant.

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